<p> Math 9 Surface Area of Prisms and Pyramids Worksheet 4-4 Journeys Page 209 Name SOLUTIONS</p><p>1. Find the surface area of the polyhedron.</p><p>Front and Back Ends Top and Bottom A = bh A = bh A = bh A = (2.5)(4.1) A = (2.5)(1.8) A = (4.1)(1.8) A = 10.25 A = 4.5 A = 7.38</p><p>Total Surface Area = 2(Rec 1) + 2(Rec 2) + 2(Rec 3) = 2(10.25) + 2(4.5) + 2(7.38) = 20.5 + 9 + 14.76 = 44.26 m2</p><p>Front and Back Ends Top and Bottom A = bh A = bh A = bh A = (14)(7) A = (14)(7) A = (14)(14) A = 98 A = 98 A = 196</p><p>Total Surface Area = 2(Rec 1) + 2(Rec 2) + 2(Rec 3) = 2(98) + 2(98) + 2(196) = 196 + 196 + 392 = 784 m2 Bottom Sides bh A = s2 A = 2 (14)(10) A = (14)2 A = 2 A = 196 A = 70</p><p>Total Surface Area = (bottom) + 4 (sides) = (196) + 4(70) = 196 + 280 = 476 cm2 Ends Side Side Side bh A = A = bh A = bh A = bh 2 30(40) A = A = (50)(91) A = (30)(91) A = (40)(91) 2 A = 600 A = 4550 A = 2730 A = 3640</p><p>Total Surface Area = 2(ends) + Side + side + side = 2(600) + 4550 + 2730 + 3640 = 3640 + 10920 = 12120 cm2 Triangle bh A = 2 (6)(5.2) A = 2 A = 15.6</p><p>Total Surface Area = 4(triangle) = 4(15.6) = 62.4 cm2</p><p>Bottom Sides bh A = s2 A = 2 (2.1)(3) A = (2.1)2 A = 2 A = 4.41 A = 3.15</p><p>Total Surface Area = (bottom) + 4 (sides) = (4.41) + 4(3.15) = 4.41 + 12.6 = 17.01 cm2 2. A rectangular prism has length x cm, width 30 cm, and height 25 cm. Its surface area is 11 950 cm2. Find its length.</p><p>Surface Area = 2(bh) + 2(bh) + 2(bh) 11 950 = 2(30)(25) + 2(30)(x) + 2(25)(x) 11950 = 1500 + 60x + 50x 11950 – 1500 = 110x 10450 = 110x 95 = x</p><p>The length is 95 cm long.</p><p>3. It costs about $10/m2 to finish the exterior of an A-frame chalet with cedar shakes and cedar wood. What is the cost to finish the exterior of this A-frame chalet?</p><p>Ends Sides Bottom bh A = A = bh A = bh 2 12(8) A = A = (15)(10) A = (12)(15) 2 A = 48 A = 150 A = 180</p><p>Total surface area = 2(ends) + 2(sides) + bottom = 2(48) + 2(150) + 180 = 96 + 300 + 180 = 576 m2 Cost = $10 x 576 = $5 760</p><p>4. The label on a 4 L can of paint says that the contents will cover an area of 40.0 m2. How many cans are needed to paint the walls and ceiling of a room 7.5 m long, 5.0 m wide, and 2.5 m tall?</p><p>Surface Area = 2(ends) + 2(sides) + (top) = 2(bh) + 2(bh) + (bh) = 2(5)(2.5) + 2(2.5)(7.5) + (5)(7.5) = 25 + 37.5 + 37.5 = 100 m2</p><p>You will need 3 cans of paint. 5. A box in the shape of a cube has a surface area of 150 m2. What are the dimensions of the box?</p><p>Surface area = 6(side) = 6(s2) Each side of the box is 5 m 150 = 6s2 long 25 = s2 5 = s</p><p>6. How much cardboard does it take to make this hatbox? The cover has a 3.0 cm rim.</p><p>Surface area = 6(triangles) + 6 (rims) + 6 (sides) bh = 12( ) + 6(bh) + 6(bh) 2  (20)(17)  = 12  + 6(20)(3) + 6(20)(30)  2  = 2040 + 360 + 3600 = 6000 cm2</p>